Digital Signal Processing Reference
In-Depth Information
Fig. 9.2
Not scaled sketch of the general altimetric inversion: an operator must find the specular
point
Q
on an a-priori surface S
0
, fulfilling three conditions (
Q
e
sct
,
Fresnel reflection). The operator then computes the geometric delay between the transmitter
T
,the
specular point
Q
, and the receiver
R
.
Straight lines
are used for simplicity, but certain operators
could also take into account the atmospheric-induced bending of the ray propagation (e.g. ray-
tracing operators)
2
P ,and
Q
2
S
0
,ande
inc
D
In order to solve the altimetric problem, an accurate knowledge of the position of
both transmitter's
T
and receiver's
R
antennas' phase centers are required, expressed
as their 3D vector with respect to the center of the Earth. We assume that both can be
obtained (Precise Orbit Determination of the GNSS transmitters, and GNSS-based
plus Inertial Navigation Systems-or others-for the receiver). In some cases it might
also be interesting to extract the receiver's altitude with respect to a reference Earth
ellipsoid H
ref
rcv
.
The general bi-static altimetric problem is slightly more complex than the mono-
static nadir-looking radar one. The inversion procedure requires a forward operator
F such that given the transmitter and receiver coordinates
T
and
R
, and given an a-
priori surface topography S
0
finds the specular point
Q
that fulfills three conditions
(see Fig.
9.2
): (1) vectors
TQ
,
QR
, and the normal at
Q
are coplanar (horizontal
gradients in the atmosphere would break this assumption); (2)
Q
2
S
0
; and (3)
e
inc
D
e
scat
(Fresnel reflection). The operator then computes the geometric range
between
T
-to-
Q
-to-
R
:
mod
geo
D
F.
T
;
R
;S
0
/
(9.2)
It is possible to correct for vertical displacements of the a-priori surface around
Q
,
S.
Q
/
D
S
0
.
Q
/
C
S
?
.
Q
/
n
.
Q
/ by linearizing around this a-priori solution, so that
the modelled range fits the measured one:
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